A1H 11.1 - Multiplication properties of Exponents

Front

What is the product of powers property of exponents?

Back

When multiplying two powers with the same base, add the exponents: a^m * a^n = a^(m+n).

Front

What is the power of a power property of exponents?

Back

When raising a power to another power, multiply the exponents: (a^m)^n = a^(m*n).

Front

What is the power of a product property of exponents?

Back

When raising a product to a power, apply the exponent to each factor: (ab)^n = a^n * b^n.

Front

What is the zero exponent property?

Back

Any non-zero base raised to the power of zero equals one: a^0 = 1 (where a ≠ 0).

Front

What is the negative exponent property?

Back

A negative exponent indicates the reciprocal of the base raised to the opposite positive exponent: a^(-n) = 1/(a^n).

Front

Simplify: (2a^2b^4z)(6a^3b^2z^5)

Back

12a^5b^6z^6.

Front

Simplify: (-4x^4y^2z^3)(7x^2y)

Back

-28x^6y^3z^3.

Front

What is the formula for the surface area of a sphere?

Back

SA = 4πr^2.

Front

If the radius of a sphere is 9a^2b^0c^3, what is the surface area?

Back

324πa^4c^6.

Front

What does it mean to simplify an expression with exponents?

Back

To rewrite the expression in a simpler form, often by combining like terms and ensuring all exponents are positive.